A TEG uses a temperature difference occurring between a hot or warm object (i.e., a heat source) and the object's colder surrounding (i.e., a heat sink) and transforms a consequential heat flow into useful electrical power. The necessary heat can be produced by radioactive materials, such as in space applications, or by sources available in the ambient, such as standard cooling/heating systems, pipe lines including pipe lines with warm waste water, surfaces of engines, parts of machines and buildings, warm-blooded animals, or human beings. Natural temperature gradients can be used, as well as geothermal temperature gradients, temperature gradients on ambient objects when naturally cooling/heating at night/day, temperature differences between a cold river and a warm shore or between a warm river and ice on it, between ice on water and surrounding air, and so on.
There is an increasing interest in miniaturized TEGs, which could replace batteries in consumer electronic products operating at low power. For example, TEGs mounted in a wristwatch have been used to generate electricity from wasted human heat, thus providing a power source for the watch itself. See M. Kishi, H. Nemoto, T. Hamao, M. Yamamoto, S. Sudou, M. Mandai and S. Yamamoto in ‘Micro-Thermoelectric Modules and Their Application to Wristwatches as an Energy Source’, Proceedings ICT'99 18th Int. Conference on Thermoelectrics, p. 301-307, 1999.
Recently, MEMS technology has also been used to fabricate miniaturized TEGs, as described by M. Strasser, R. Aigner, C. Lauterbach, T. F. Sturm, M. Franosh and G. Wachutka in ‘Micromachined CMOS Thermoelectric Generators as On-chip Power Supply’, Transducers '03. 12th International Conference on Solid State Sensors, Actuators and Microsystems, p. 45-48, 2003; by A. Jacquot, W. L. Liu, G. Chen, J.-P. Fleurial, A. Dausher, B. Lenoir in ‘Fabrication and modeling of an in-plane thermoelectric micro-generator’, Proceedings ICT '02. 21st International Conference on Thermoelectrics, p. 561-564, 2002; and by H. Böttner, A. Schubert, K. H. Schlereth, D. Eberhard, A. Gavrikov, M. Jägle, G. Kühner, C. Künzel, J. Nurnur and G. Plesher in ‘New Thermoelectric Components using Micro-System-Technologies’, ETS 2001-6th European Workshop on Thermoelectrics, 2001.
TEGs can be characterized by an electrical and a thermal resistance, and by both voltage and power generated per unit temperature difference between the hot and cold sides of the TEG. The relative importance of these factors depends on the specific application. In general, electrical resistance should be low, and voltage or power output should be maximized, in particular, in applications with a small temperature difference (i.e., a few degrees C. or few tens of degrees C.). If a fixed temperature difference is imposed at the boundaries of the TEG by, for example, means of hot and cold plates, the value of thermal resistance is not crucial. Contrary thereto, if the boundary condition is a fixed or limited heat flow through the device, then the thermal resistance, on one hand, has to be large enough to generate a reasonable temperature drop over the device, but on the other hand, has to be small enough to avoid variations in the heat flow.
The basic element of a TEG is a thermocouple 10 (FIG. 1). An example of a thermocouple 10 includes a first leg 11 and a second leg 12 formed with two different thermoelectric materials, such as the same but opposite doped semiconductor material, and exhibiting low thermal conductance and low electrical resistance. For example, the legs 11, 12 could be formed from BiTe. If the first leg 11 is formed of n-type BiTe, then the second leg 12 is formed of p-type BiTe, and vice versa. The legs 11, 12 are connected by a conductive interconnect, such as a metal layer interconnect 13, which forms a low-resistance ohmic contact to the semiconductor legs 11, 12.
In FIG. 2, a TEG 20 including a thermopile 21 having a plurality of, and preferably a large number, of thermocouples 10 is shown. The thermopile 21 is sandwiched between a hot plate 22 and a cold plate 23. The hot plate 22 and the cold plate 23 are made of materials having a large thermal conductivity, so that the thermal conductance of the plates 22, 23 is much larger (at least a factor of ten) than the total thermal conductance of the thermopile 21.
Hereinafter, the difference between classical and micromachined thermoelectric generators is discussed. Although the geometrical arrangement of the basic elements or thermocouples 10 composing the TEG 20 may be different, such as the in-plane position of the thermocouples 10 (i.e., parallel to the plates 22, 23), in classical and micromachined TEGs 20 the schemes of FIG. 1 and FIG. 2 hold for both. The difference between the two implementations is quantitative.
Typical dimensions of legs 11, 12 for a classical TEG 20 are on the order of a few millimeters for the height h and on the order of hundreds of micrometers to 1 millimeter for the square root of the cross-section, which in the further description will be referred to as lateral size a. The aspect ratio of the legs 11, 12, which is determined by height h over lateral size a (h/a), may be in the order of 1 to 3 in case of a classical TEG 20. The aspect ratio for a TEG produced by Seiko, i.e., a classical TEG, is 7.5. The smallest thermopiles 10 currently available on the market (Thermix; Kiev, Ukraine) demonstrate an aspect ratio of less than 5. For micromachined TEGs 20, the lateral size a is on the order of a few micrometer, and the aspect ratio h/a can be larger than in the case of a classical TEG (e.g., more than 10).
In case of a constant or limited heat flow through the TEG 20, the output voltage and power depend on the number of thermocouples 10 comprised in it, and it can easily be shown that the maximum power is obtained when the heat flow through the thermoelectric material is equal to the “parasitic” heat flow through the air, including radiation heat exchange.
In order to give numerical examples, the TEG device area is fixed to 1 cm2 and the heat flow to 18.5 mW/cm2, which is a typical heat flow from a human body skin. Furthermore, it is assumed that the legs 11, 12 of the thermocouples 10 are respectively made of n-type and p-type BiTe, and that the TEG 20 operates in air. The thermal resistance of the metal layer interconnect 13 and the electrical resistance of the contacts between the legs 11, 12 of the thermocouple 10 and the metal layer interconnect 13 are considered to be negligible. Values used for the calculations are reported in Table I.
TABLE IParameters used for the calculation of TEG performanceParametersValueThermal conductivity of BiTe, W K−1m−1 1.5Thermal conductivity of air, W K−1m−1 0.026Resistivity of BiTe (n and p), Ωm 10−5Input heat flow, Wm−2185
First, a classical TEG 20 is considered. Dimensions chosen for the legs 11, 12 are close to those of the best currently available commercial devices, i.e., a lateral size a of 250 μm and a height h of 750 μm. In FIG. 3, the output power Pout (full line) and output voltage Vout (dashed line) for such a TEG 20 are illustrated as a function of the number of thermocouples 10. In correspondence of the maximum power, the output voltage is low (i.e., 15 mV) as can be seen from FIG. 3, which is well below the level necessary for powering standard electronics. Typical voltages are 3 to 5 V. It is well known in the art to up-convert 800 mV to these values; however, it is much more difficult and less efficient to reach these values starting from 300 mV or less.
As can be seen in FIG. 4, the temperature drop corresponding to the maximum power is about 2.3 K. The performance of the TEG 20 can be improved by increasing the aspect ratio of the legs 11, 12. For example, as described by M. Kishi, H. Nemoto, T. Hamao, M. Yamamoto, S. Sudou, M. Mandai and S. Yamamoto in ‘Micro-Thermoelectric Modules and Their Application to Wristwatches as an Energy Source’, Proceedings ICT'99 18th Int. Conference on Thermoelectrics, p. 301-307, 1999, the lateral size a and height h of the legs 11, 12 are respectively 80 μm and 600 μm. In this case, a 0.4 cm2 TEG (10 units of 2×2 mm size are used in the watch) gives a voltage of 0.25 V when it delivers a maximum power of about 20 μW. Although the aspect ratio, h/a, of the thermoelectric legs 11, 12 of 7.5 (=600 μm/80 μm) in the above example represents a current technological limit, the voltage obtained is still of impractical use. It can thus be concluded that the low output voltage is a main restriction to a wide use of the TEGs 20 operated in a low heat flow mode.
Next, a micromachined TEG 20 is considered which comprises legs with a thickness of 0.5 μm, a width of 1 μm and a height of 5 μm. In FIG. 5, the output power (∘) and voltage (▴) are shown as a function of the number of thermocouples 10. The power is limited to only 0.11 μW. This maximal power is achieved for a TEG 20 having about 1.8 million thermocouples 10 (see FIG. 5). For the same number of thermocouples 10, a voltage of about 3V is obtained. In FIG. 6, the temperature difference (∘) and the electrical resistance (▴) of a micromachined TEG 20 are reported. The temperature difference (∘) of the TEG 20 at the maximal power is limited to 18 mK. The corresponding thermal resistance, which is determined by Rth=ΔT/P (with ΔT=a temperature drop and P the heat flow) is 1 K/W, which is not enough to obtain a good temperature drop.
The above results are confirmed by experimental data. For example, as described by M. Strasser, R. Aigner, C. Lauterbach, T. F. Sturm, M. Franosh and G. Wachutka in ‘Micromachined CMOS Thermoelectric Generators as On-chip Power Supply’, Transducers '03, 12th International Conference on Solid State Sensors, Actuators and Microsystems, p. 45-48, 2003, a large number of thermocouples 10 has been fabricated and a large output voltage is obtained. H. Böttner, A. Schubert, K. H. Schlereth, D. Eberhard, A. Gavrikov, M. Jägle, G. Kühner, C. Künzel, J. Nurnur and G. Plesher point out in ‘New Thermoelectric Components using Micro-System-Technologies’, ETS 2001—6th European Workshop on Thermoelectrics, 2001, that both the temperature drop and the output power are low in micromachined TEGs 20. For example, micromachined TEGs produced by Infineon show about 10 mK temperature difference between the hot and the cold side (H. Böttner in ‘Thermoelectric Micro Devices: Current State, Recent Developments and future Aspects for Technological Progress and Applications’, International Conference on Thermoelectrics, 2002). However, experimental conditions have not been published.
For the number of thermocouples 10 at which the maximum power is achieved (see FIG. 5), the electrical resistance approaches 0.4 GΩ (see FIG. 6), which is a too high of a value for a generator powering electronic devices or battery chargers. It can be seen that the optimal number of thermocouples 10 is about 1.8 million, because in that case the thermal resistance of air is equal to the thermal resistance of thermopile or in series connected thermocouples 10, so the output power is maximized. This large number of thermocouples 10 can be fabricated if one thermocouple 10 occupies a square of only about 7×7 μm2 size. This is a difficult but not impossible task. The large number of thermocouples 10 furthermore has the drawback of increased probability of getting a non-functioning device, since thermocouples 10 are electrically coupled in series. Hence, the failure of one thermocouple 10 will cause the failure of the whole TEG 20. This drawback potentially leads to a dramatically decreased yield of good devices and increased cost of manufacturing.
In order to understand the difference in behavior between a classical and a micromachined TEG 20, a thermal analysis is performed of the TEG configuration as illustrated in FIG. 2. Analytical results are reported and discussed hereinafter. The number of thermocouples n, the temperature drop ΔT, and the output voltage Vout at a maximal power Pout are given by the expressions (1) to (4):
                              n          =                                                                      G                  air                                ⁢                h                                                              g                  te                                ⁢                                  a                  2                                                      =                                          Ag                a                                                              g                  te                                ⁢                                  a                  2                                                                    ,                            (        1        )                                                      P            out                    =                                                    1                16                            ⁢                              S                2                            ⁢                                                                    W                    u                    2                                    ⁢                                      A                    2                                                                                        g                    te                                    ⁢                  ρ                                            ⁢                              1                                  G                  air                                                      =                                          1                16                            ⁢                              S                2                            ⁢                                                                    W                    u                    2                                    ⁢                  A                                                                      g                    te                                    ⁢                  ρ                                            ⁢                              h                                  g                  a                                                                    ,                            (        2        )                                                      Δ            ⁢                                                  ⁢            T                    =                                                                      W                  u                                ⁢                A                                            2                ⁢                                  G                  air                                                      =                                                            W                  u                                ⁢                h                                            2                ⁢                                  g                  a                                                                    ,                            (        3        )                                          V          =                                                                      W                  u                                ⁢                AS                                            g                te                                      ⁢                          h                              a                2                                                    ,                            (        4        )            wherein                A is the area of the hot/cold plate 22, 23,        a is the lateral size of the legs 11, 12,        h is the height of the legs 11, 12,        ga is the thermal conductivity of air,        gte is the thermal conductivity of the thermoelectric material the legs 11, 12 are made of,        ρ is the resistivity of the thermoelectric material the legs 11, 12 are made of,        S is the Seebeck coefficient (assumed to be equal for both legs 11, 12),        Gair is the thermal conductance of the air between the hot plate 22 and the cold plate 23, and        Wu is heat flow per unit area.        
Equations (1) and (2) show that, at the maximum power condition, the number n of necessary thermocouples and the output voltage depends on the ratio h/a2, which is much larger for a micromachined TEG than for a classical one. It can then be stated that micromachined thermoelectric generators require a larger number of thermocouples and deliver power at a larger voltage. The power Pout and temperature difference ΔT (respectively, equations (2) and (3)) depend mainly on the thermal conductance Gair of the air between hot plate and the cold plate. Since this thermal conductance Gair is larger for micromachined thermopiles, the temperature drop ΔT and power Pout are low for these devices.